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Campoamor-Stursberg, Rutwig and Montigny, Marc de and Traubenberg, Michel Rausch de
(2022)
*an overview of generalised Kac-Moody algebras on compact real mainfolds.*
Journal of geometry and physics, 180
.
ISSN 0393-0440

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Official URL: https://doi.org/10.1016/j.geomphys.2022.104624

## Abstract

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a Fourier expansion. The Peter–Weyl theorem for the case of manifolds related to compact Lie groups and coset spaces is discussed, and appropriate Hilbert bases for the space of square-integrable functions are constructed. It is shown that such bases are characterised by the representation theory of the compact Lie group, from which a complete set of labelling operator is obtained. The existence of central extensions of generalised Kac-Moody algebras is analysed using a duality property of Hermitian operators on the manifold, and the corresponding root systems are constructed. Several applications of physically relevant compact groups and coset spaces are discussed.

Item Type: | Article |
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Uncontrolled Keywords: | Centrally extended infinite dimensional Lie algebras; Peter-Weyl theorem and the labelling problem; Fourier expansion on compact manifolds and coset spaces |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 74772 |

Deposited On: | 27 Sep 2022 07:58 |

Last Modified: | 27 Sep 2022 08:33 |

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